Heat the oil in a large pot over medium-high heat. Sauté the mushrooms and onion for 5–6 minutes, until soft. Add the garlic and cook for 1 minute, until fragrant.
Stir in the flour. Add ¼ cup broth and scrape up the browned bits.
Whisk the arrowroot into the milk until smooth. Add to the pot with the potatoes, remaining broth, thyme, salt, oregano, and pepper.
Bring to a boil, then reduce heat to medium-low and cover. Cook for 20–30 minutes, stirring occasionally, until thickened and the potatoes are tender.
Turn off the heat and stir in the spinach. Garnish with red pepper flakes, thyme, parsley, or chives if desired.